Given a biconnected planar graph G and a pair of vertices s and t, the two disjoint problem asks to find a pair of internally disjoint paths from s to t. We present a simple and efficient parallel algorithm for the same. Our algorithm uses the notion of bridges in a novel way and this results in a more elegant and simple algorithm than the existing one. The all-bidirectional-edges (ABE) problem is to find an edge labeling such that an edge (u, v) in E is labeled 〈u, v〉 or 〈v, u〉 or both depending on the existence of a simple path from s to t that visits the vertices in the order u, v or v, u or both, respectively. We present an optimal parallel algorithm for the same. © 1995.
Srikrishna, G., & Rangan, C. P. (1995). Optimal parallel algorithms for path problems on planar graphs. Theoretical Computer Science, 145(1–2), 27–43. https://doi.org/10.1016/0304-3975(94)00189-P